few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

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options: Develop understanding of statistical variability.

Calculate expected values and use them to solve problems.

Understand independence and conditional probability and use them to interpret data.

Use random sampling to draw inferences about a population.

Investigate chance processes and develop, use, and evaluate probability models.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Interpret linear models.

Use probability to evaluate outcomes of decisions.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on a single count or measurement variable.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Investigate patterns of association in bivariate data.
problem_activity: Warm-up
The purpose of this warm-up is to encourage students to connect the ideas they learned earlier about statistical questions and types of data (categorical and numerical) to the work on describing distributions (center and spread).
There are many ways to interpret the questions and identify how each one is unique. For example, they could say that Question A is about retirement, Question B about jobs, etc. If students begin to depart from thinking in statistical terms, remind them to think about how we might go about answering the questions and what the answers might involve.
Launch
Arrange students in groups of 2–4. Display the questions for all to see. Give students 1 minute of quiet think time and ask students to indicate when they have noticed one question that does not belong and can explain why. When the minute is up, give students 2 minutes to share with their group their reasoning on why a question doesn't belong, and then, together, find at least one reason each question doesn't belong.
Student Facing
Here are four questions about the population of Alaska. Which question does not belong? Be prepared to explain your reasoning.
In general, at what age do Alaska residents retire?
At what age can Alaskans vote?
What is the age difference between the youngest and oldest Alaska residents with a full-time job?
Which age group is the largest part of the population: 18 years or younger, 19–25 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, or 65 years or older?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Ask each group to share one reason why a particular question does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer for why a question does not belong, attend to students’ explanations and ensure the reasons given are correct.
If students use terms that are essential in this unit (such as center, spread, statistical, non-statistical, numerical data, categorical data, etc.), ask them to explain their meanings in their own words; these are opportunities to reinforce their understanding of the terms and to note any misconceptions. If students give unsubstantiated claims, ask them to substantiate them.


correct_option_index: 0

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